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Authors: GHANIA HADJI, YAMINA LASKRI, TAHAR BECHOUAT, RACHID BENZINE.
Received 18 February 2022; Accepted 27 April 2022.
pp. 457-468
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The Conjugate Gradient (CG) method is a powerful iterative approach for solving large-scale minimization problems, characterized by its simplicity, low computation cost and good convergence. In this paper, a new hybrid conjugate gradient HLB method (HLB: Hadji-Laskri-Bechouat) is proposed and analysed for unconstrained optimization. We compute the parameter Ξ²HLBkπ½ππ»πΏπ΅ as a convex combination of the Polak-Ribi`{e}re-Polyak (Ξ²PRPk)[1](π½πππ π)[1] and the Mohd Rivaie-Mustafa Mamat and Abdelrhaman Abashar (Ξ²RMIL+k)(π½ππ ππΌπΏ+) i.e Ξ²HLBk=(1βΞΈk)Ξ²PRPk+ΞΈkΞ²RMIL+kπ½ππ»πΏπ΅=(1βππ)π½πππ π+πππ½ππ ππΌπΏ+. By comparing numerically CGHLB with PRP and RMIL+ and by using the Dolan and More CPU performance, we deduce that CGHLB is more efficient.
Mathematics Subject Classification (2010): 90C26, 65H10, 65K05, 90C26, 90C06.
Keywords: Unconstrained optimization, hybrid conjugate gradient method, line search, descent property, global convergence.
